32-digit values of the first 65 recurrence coefficients for the weight function w(x)=exp(-x)*log(1+1/x) on [1,Inf]

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By Walter Gautschi

Purdue University

32-digit values of the first 65 recurrence coefficients for the weight function w(x)=x^a*exp(-x)*log(1+1/x) on [1,Inf], a=0

Version 1.0 - published on 09 May 2017 doi:10.4231/R7028PJT - cite this Archived on 10 Jun 2017

Licensed under Attribution 3.0 Unported

Description

32-digit values of the first 65 recurrence coefficients for orthogonal polynomials relative to the weight function w(x)=x^a*exp(-x)*log(1+1/x) on [1,Inf], a=0, are computed by a 1-component discretization method using the routine sr_explog1inf(32,65), where dig=36 has to be entered when prompted by the routine. The value 36 of dig has been determined by the routine dig_explog1inf(65,32,4,32). Both routines, dig_explog1inf.m and sr_explog1inf.m, may take many hours to run, the former as much as 19 hours, the latter about 12 hours. The software provided in this dataset allows generating any number N of recurrence coefficients for any a > -1 not an integer, as well as for different precisions, as long as there is no error message "Mcap exceeds Mmax in smcdis with irout=1", indicating lack of convergence in the discretization procedure.

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The dataset consists of one text file and eight Matlab scripts.

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